LMFDB - Embedded newform 896.2.bh.a.81.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [896,2,Mod(81,896)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(896, base_ring=CyclotomicField(24))

chi = DirichletCharacter(H, H._module([0, 9, 16]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("896.81");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 896 = 2^{7} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	896.bh (of order $24$, degree $8$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$7.15459602111$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$30$ over $\Q(\zeta_{24})$
Twist minimal:	no (minimal twist has level 224)
Sato-Tate group:	$\mathrm{SU}(2)[C_{24}]$

Embedding invariants

Embedding label			81.15
Character	$\chi$	$=$	896.81
Dual form			896.2.bh.a.177.15

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.112695 + 0.0864738i) q^{3} +(1.22200 - 1.59255i) q^{5} +(1.93515 - 1.80422i) q^{7} +(-0.771235 + 2.87829i) q^{9} +O(q^{10})$	\(q+(-0.112695 + 0.0864738i) q^{3} +(1.22200 - 1.59255i) q^{5} +(1.93515 - 1.80422i) q^{7} +(-0.771235 + 2.87829i) q^{9} +(-0.737665 + 5.60312i) q^{11} +(-1.67953 + 4.05474i) q^{13} +0.285143i q^{15} +(1.41287 + 0.815720i) q^{17} +(5.25122 - 0.691336i) q^{19} +(-0.0620631 + 0.370666i) q^{21} +(0.283964 - 1.05977i) q^{23} +(0.251185 + 0.937436i) q^{25} +(-0.325061 - 0.784767i) q^{27} +(4.82760 + 1.99966i) q^{29} +(1.15574 - 2.00180i) q^{31} +(-0.401392 - 0.695231i) q^{33} +(-0.508549 - 5.28657i) q^{35} +(1.87037 - 2.43752i) q^{37} +(-0.161354 - 0.602183i) q^{39} +(-8.26270 - 8.26270i) q^{41} +(3.66118 - 1.51651i) q^{43} +(3.64135 + 4.74550i) q^{45} +(10.4696 - 6.04464i) q^{47} +(0.489578 - 6.98286i) q^{49} +(-0.229761 + 0.0302486i) q^{51} +(-0.862860 + 6.55407i) q^{53} +(8.02180 + 8.02180i) q^{55} +(-0.532003 + 0.532003i) q^{57} +(-5.25402 - 0.691705i) q^{59} +(0.229695 + 1.74471i) q^{61} +(3.70061 + 6.96138i) q^{63} +(4.40497 + 7.62963i) q^{65} +(-8.82073 + 6.76838i) q^{67} +(0.0596408 + 0.143986i) q^{69} +(-4.00484 + 4.00484i) q^{71} +(8.45624 - 2.26584i) q^{73} +(-0.109371 - 0.0839233i) q^{75} +(8.68177 + 12.1738i) q^{77} +(2.01864 - 1.16546i) q^{79} +(-7.63731 - 4.40940i) q^{81} +(-5.65524 + 13.6529i) q^{83} +(3.02560 - 1.25324i) q^{85} +(-0.716964 + 0.192110i) q^{87} +(0.381246 + 0.102154i) q^{89} +(4.06551 + 10.8767i) q^{91} +(0.0428573 + 0.325534i) q^{93} +(5.31602 - 9.20762i) q^{95} +13.5272 q^{97} +(-15.5585 - 6.44453i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q + 4 q^{3} - 4 q^{5} + 8 q^{7} - 4 q^{9}+O(q^{10}) $ 240 * q + 4 * q^3 - 4 * q^5 + 8 * q^7 - 4 * q^9	$ 240 q + 4 q^{3} - 4 q^{5} + 8 q^{7} - 4 q^{9} + 4 q^{11} - 16 q^{13} + 4 q^{19} - 8 q^{21} + 12 q^{23} - 4 q^{25} + 16 q^{27} - 16 q^{29} + 56 q^{31} - 8 q^{33} + 32 q^{35} - 4 q^{37} + 4 q^{39} - 16 q^{41} + 8 q^{45} + 28 q^{51} - 20 q^{53} + 16 q^{55} - 16 q^{57} + 36 q^{59} - 4 q^{61} + 16 q^{63} - 8 q^{65} - 36 q^{67} - 16 q^{69} - 48 q^{71} - 4 q^{73} - 16 q^{75} - 8 q^{77} + 96 q^{83} - 56 q^{85} + 4 q^{87} - 4 q^{89} + 56 q^{91} + 20 q^{93} + 8 q^{95} - 32 q^{97} - 8 q^{99}+O(q^{100}) $ 240 * q + 4 * q^3 - 4 * q^5 + 8 * q^7 - 4 * q^9 + 4 * q^11 - 16 * q^13 + 4 * q^19 - 8 * q^21 + 12 * q^23 - 4 * q^25 + 16 * q^27 - 16 * q^29 + 56 * q^31 - 8 * q^33 + 32 * q^35 - 4 * q^37 + 4 * q^39 - 16 * q^41 + 8 * q^45 + 28 * q^51 - 20 * q^53 + 16 * q^55 - 16 * q^57 + 36 * q^59 - 4 * q^61 + 16 * q^63 - 8 * q^65 - 36 * q^67 - 16 * q^69 - 48 * q^71 - 4 * q^73 - 16 * q^75 - 8 * q^77 + 96 * q^83 - 56 * q^85 + 4 * q^87 - 4 * q^89 + 56 * q^91 + 20 * q^93 + 8 * q^95 - 32 * q^97 - 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/896\mathbb{Z}\right)^\times$.

$n$	$127$	$129$	$645$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{3}{8}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		0			0
$2$		0			0
$3$	−0.112695	+	0.0864738i	−0.0650644	+	0.0499257i	−0.640782	−	0.767723i	$-0.721390\pi$
$3$	−0.112695	+	0.0864738i	−0.0650644	+	0.0499257i	0.575717	+	0.817649i	$0.304723\pi$
$4$		0			0
$5$	1.22200	−	1.59255i	0.546497	−	0.712208i	−0.435694	−	0.900095i	$-0.643497\pi$
$5$	1.22200	−	1.59255i	0.546497	−	0.712208i	0.982191	+	0.187887i	$0.0601637\pi$
$6$		0			0
$7$	1.93515	−	1.80422i	0.731416	−	0.681931i
$7$	1.93515	−	1.80422i	0.731416	−	0.681931i
$8$		0			0
$9$	−0.771235	+	2.87829i	−0.257078	+	0.959429i
$10$		0			0
$11$	−0.737665	+	5.60312i	−0.222414	+	1.68940i	0.407870	+	0.913040i	$0.366272\pi$
$11$	−0.737665	+	5.60312i	−0.222414	+	1.68940i	−0.630285	+	0.776364i	$0.717062\pi$
$12$		0			0
$13$	−1.67953	+	4.05474i	−0.465817	+	1.12458i	0.500155	+	0.865936i	$0.333276\pi$
$13$	−1.67953	+	4.05474i	−0.465817	+	1.12458i	−0.965972	+	0.258646i	$0.916724\pi$
$14$		0			0
$15$			0.285143i			0.0736236i
$16$		0			0
$17$	1.41287	+	0.815720i	0.342671	+	0.197841i	0.661452	−	0.749987i	$-0.269940\pi$
$17$	1.41287	+	0.815720i	0.342671	+	0.197841i	−0.318782	+	0.947828i	$0.603274\pi$
$18$		0			0
$19$	5.25122	−	0.691336i	1.20471	−	0.158603i	0.498682	−	0.866785i	$-0.333818\pi$
$19$	5.25122	−	0.691336i	1.20471	−	0.158603i	0.706030	+	0.708182i	$0.250484\pi$
$20$		0			0
$21$	−0.0620631	+	0.370666i	−0.0135433	+	0.0808859i
$22$		0			0
$23$	0.283964	−	1.05977i	0.0592106	−	0.220977i	−0.929981	−	0.367609i	$-0.880177\pi$
$23$	0.283964	−	1.05977i	0.0592106	−	0.220977i	0.989191	+	0.146632i	$0.0468433\pi$
$24$		0			0
$25$	0.251185	+	0.937436i	0.0502371	+	0.187487i
$26$		0			0
$27$	−0.325061	−	0.784767i	−0.0625581	−	0.151029i
$28$		0			0
$29$	4.82760	+	1.99966i	0.896464	+	0.371327i	0.782859	−	0.622199i	$-0.213760\pi$
$29$	4.82760	+	1.99966i	0.896464	+	0.371327i	0.113604	+	0.993526i	$0.463760\pi$
$30$		0			0
$31$	1.15574	−	2.00180i	0.207577	−	0.359534i	−0.743374	−	0.668876i	$-0.766776\pi$
$31$	1.15574	−	2.00180i	0.207577	−	0.359534i	0.950951	+	0.309342i	$0.100109\pi$
$32$		0			0
$33$	−0.401392	−	0.695231i	−0.0698734	−	0.121024i
$34$		0			0
$35$	−0.508549	−	5.28657i	−0.0859605	−	0.893594i
$36$		0			0
$37$	1.87037	−	2.43752i	0.307487	−	0.400725i	−0.613892	−	0.789390i	$-0.710397\pi$
$37$	1.87037	−	2.43752i	0.307487	−	0.400725i	0.921379	+	0.388665i	$0.127064\pi$
$38$		0			0
$39$	−0.161354	−	0.602183i	−0.0258374	−	0.0964265i
$40$		0			0
$41$	−8.26270	−	8.26270i	−1.29042	−	1.29042i	−0.934528	−	0.355889i	$-0.884178\pi$
$41$	−8.26270	−	8.26270i	−1.29042	−	1.29042i	−0.355889	−	0.934528i	$-0.615822\pi$
$42$		0			0
$43$	3.66118	−	1.51651i	0.558325	−	0.231266i	−0.0856330	−	0.996327i	$-0.527291\pi$
$43$	3.66118	−	1.51651i	0.558325	−	0.231266i	0.643958	+	0.765061i	$0.277291\pi$
$44$		0			0
$45$	3.64135	+	4.74550i	0.542821	+	0.707418i
$46$		0			0
$47$	10.4696	−	6.04464i	1.52715	−	0.881701i	0.527671	−	0.849449i	$-0.323065\pi$
$47$	10.4696	−	6.04464i	1.52715	−	0.881701i	0.999480	−	0.0322524i	$-0.0102680\pi$
$48$		0			0
$49$	0.489578	−	6.98286i	0.0699397	−	0.997551i
$50$		0			0
$51$	−0.229761	+	0.0302486i	−0.0321730	+	0.00423566i
$52$		0			0
$53$	−0.862860	+	6.55407i	−0.118523	+	0.900271i	0.824108	+	0.566433i	$0.191677\pi$
$53$	−0.862860	+	6.55407i	−0.118523	+	0.900271i	−0.942631	+	0.333838i	$0.891656\pi$
$54$		0			0
$55$	8.02180	+	8.02180i	1.08166	+	1.08166i
$56$		0			0
$57$	−0.532003	+	0.532003i	−0.0704655	+	0.0704655i
$58$		0			0
$59$	−5.25402	−	0.691705i	−0.684016	−	0.0900524i	−0.219494	−	0.975614i	$-0.570440\pi$
$59$	−5.25402	−	0.691705i	−0.684016	−	0.0900524i	−0.464522	+	0.885562i	$0.653774\pi$
$60$		0			0
$61$	0.229695	+	1.74471i	0.0294095	+	0.223387i	0.999838	−	0.0180016i	$-0.00573040\pi$
$61$	0.229695	+	1.74471i	0.0294095	+	0.223387i	−0.970428	+	0.241389i	$0.922397\pi$
$62$		0			0
$63$	3.70061	+	6.96138i	0.466233	+	0.877052i
$64$		0			0
$65$	4.40497	+	7.62963i	0.546369	+	0.946339i
$66$		0			0
$67$	−8.82073	+	6.76838i	−1.07762	+	0.826890i	−0.985638	−	0.168871i	$-0.945988\pi$
$67$	−8.82073	+	6.76838i	−1.07762	+	0.826890i	−0.0919853	+	0.995760i	$0.529321\pi$
$68$		0			0
$69$	0.0596408	+	0.143986i	0.00717991	+	0.0173338i
$70$		0			0
$71$	−4.00484	+	4.00484i	−0.475287	+	0.475287i	−0.903621	−	0.428334i	$-0.859101\pi$
$71$	−4.00484	+	4.00484i	−0.475287	+	0.475287i	0.428334	+	0.903621i	$0.359101\pi$
$72$		0			0
$73$	8.45624	−	2.26584i	0.989728	−	0.265197i	0.272592	−	0.962130i	$-0.412119\pi$
$73$	8.45624	−	2.26584i	0.989728	−	0.265197i	0.717136	+	0.696933i	$0.245453\pi$
$74$		0			0
$75$	−0.109371	−	0.0839233i	−0.0126291	−	0.00969062i
$76$		0			0
$77$	8.68177	+	12.1738i	0.989380	+	1.38733i
$78$		0			0
$79$	2.01864	−	1.16546i	0.227115	−	0.131125i	−0.382126	−	0.924110i	$-0.624808\pi$
$79$	2.01864	−	1.16546i	0.227115	−	0.131125i	0.609240	+	0.792986i	$0.291474\pi$
$80$		0			0
$81$	−7.63731	−	4.40940i	−0.848590	−	0.489934i
$82$		0			0
$83$	−5.65524	+	13.6529i	−0.620743	+	1.49861i	0.230090	+	0.973169i	$0.426098\pi$
$83$	−5.65524	+	13.6529i	−0.620743	+	1.49861i	−0.850833	+	0.525436i	$0.823902\pi$
$84$		0			0
$85$	3.02560	−	1.25324i	0.328172	−	0.135933i
$86$		0			0
$87$	−0.716964	+	0.192110i	−0.0768666	+	0.0205964i
$88$		0			0
$89$	0.381246	+	0.102154i	0.0404120	+	0.0108284i	0.278968	−	0.960300i	$-0.410008\pi$
$89$	0.381246	+	0.102154i	0.0404120	+	0.0108284i	−0.238556	+	0.971129i	$0.576674\pi$
$90$		0			0
$91$	4.06551	+	10.8767i	0.426181	+	1.14019i
$92$		0			0
$93$	0.0428573	+	0.325534i	0.00444410	+	0.0337563i
$94$		0			0
$95$	5.31602	−	9.20762i	0.545412	−	0.944682i
$96$		0			0
$97$	13.5272			1.37348			0.686738	−	0.726905i	$-0.259042\pi$
$97$	13.5272			1.37348			0.686738	+	0.726905i	$0.259042\pi$
$98$		0			0
$99$	−15.5585	−	6.44453i	−1.56369	−	0.647700i
$100$		0			0
$101$	1.13933	+	0.149995i	0.113367	+	0.0149251i	0.186996	−	0.982361i	$-0.440125\pi$
$101$	1.13933	+	0.149995i	0.113367	+	0.0149251i	−0.0736291	+	0.997286i	$0.523458\pi$
$102$		0			0
$103$	−11.5506	−	3.09497i	−1.13811	−	0.304956i	−0.359921	−	0.932983i	$-0.617196\pi$
$103$	−11.5506	−	3.09497i	−1.13811	−	0.304956i	−0.778192	+	0.628027i	$0.783863\pi$
$104$		0			0
$105$	0.514461	+	0.551793i	0.0502062	+	0.0538495i
$106$		0			0
$107$	2.14728	+	1.64767i	0.207586	+	0.159286i	0.707322	−	0.706891i	$-0.249903\pi$
$107$	2.14728	+	1.64767i	0.207586	+	0.159286i	−0.499736	+	0.866178i	$0.666570\pi$
$108$		0			0
$109$	−10.5564	−	13.7574i	−1.01112	−	1.31772i	−0.947504	−	0.319745i	$-0.896403\pi$
$109$	−10.5564	−	13.7574i	−1.01112	−	1.31772i	−0.0636179	−	0.997974i	$-0.520264\pi$
$110$		0			0
$111$			0.436434i			0.0414244i
$112$		0			0
$113$		−	11.2054i		−	1.05411i	−0.849830	−	0.527056i	$-0.823296\pi$
$113$		−	11.2054i		−	1.05411i	0.849830	−	0.527056i	$-0.176704\pi$
$114$		0			0
$115$	−1.34072	−	1.74726i	−0.125023	−	0.162933i
$116$		0			0
$117$	−10.3754	−	7.96132i	−0.959205	−	0.736024i
$118$		0			0
$119$	4.20584	−	0.970589i	0.385549	−	0.0889737i
$120$		0			0
$121$	−20.2256	−	5.41944i	−1.83869	−	0.492676i
$122$		0			0
$123$	1.64567	+	0.216657i	0.148385	+	0.0195353i
$124$		0			0
$125$	11.0727	+	4.58644i	0.990368	+	0.410224i
$126$		0			0
$127$	8.87926			0.787907			0.393954	−	0.919130i	$-0.371107\pi$
$127$	8.87926			0.787907			0.393954	+	0.919130i	$0.371107\pi$
$128$		0			0
$129$	−0.281458	+	0.487499i	−0.0247810	+	0.0429219i
$130$		0			0
$131$	0.413648	+	3.14197i	0.0361406	+	0.274515i	0.999968	+	0.00798837i	$0.00254280\pi$
$131$	0.413648	+	3.14197i	0.0361406	+	0.274515i	−0.963827	+	0.266527i	$0.914124\pi$
$132$		0			0
$133$	8.91455	−	10.8122i	0.772990	−	0.937536i
$134$		0			0
$135$	−1.64700	−	0.441313i	−0.141752	−	0.0379822i
$136$		0			0
$137$	−8.83587	+	2.36756i	−0.754899	+	0.202275i	−0.615690	−	0.787988i	$-0.711123\pi$
$137$	−8.83587	+	2.36756i	−0.754899	+	0.202275i	−0.139209	+	0.990263i	$0.544456\pi$
$138$		0			0
$139$	3.94283	−	1.63317i	0.334427	−	0.138524i	−0.209150	−	0.977884i	$-0.567070\pi$
$139$	3.94283	−	1.63317i	0.334427	−	0.138524i	0.543577	+	0.839360i	$0.317070\pi$
$140$		0			0
$141$	−0.657169	+	1.58655i	−0.0553436	+	0.133611i
$142$		0			0
$143$	−21.4802	−	12.4016i	−1.79627	−	1.03708i
$144$		0			0
$145$	9.08390	−	5.24459i	0.754377	−	0.435540i
$146$		0			0
$147$	0.548661	+	0.829268i	0.0452528	+	0.0683968i
$148$		0			0
$149$	11.0871	+	8.50740i	0.908287	+	0.696953i	0.953297	−	0.302033i	$-0.0976654\pi$
$149$	11.0871	+	8.50740i	0.908287	+	0.696953i	−0.0450104	+	0.998987i	$0.514332\pi$
$150$		0			0
$151$	−2.05182	+	0.549783i	−0.166975	+	0.0447407i	−0.341338	−	0.939941i	$-0.610880\pi$
$151$	−2.05182	+	0.549783i	−0.166975	+	0.0447407i	0.174363	+	0.984681i	$0.444213\pi$
$152$		0			0
$153$	−3.43753	+	3.43753i	−0.277908	+	0.277908i
$154$		0			0
$155$	−1.77564	−	4.28678i	−0.142623	−	0.344322i
$156$		0			0
$157$	−1.13884	+	0.873863i	−0.0908894	+	0.0697419i	−0.653207	−	0.757180i	$-0.726577\pi$
$157$	−1.13884	+	0.873863i	−0.0908894	+	0.0697419i	0.562317	+	0.826922i	$0.309910\pi$
$158$		0			0
$159$	−0.469516	−	0.813225i	−0.0372350	−	0.0644929i
$160$		0			0
$161$	−1.36254	−	2.56314i	−0.107383	−	0.202004i
$162$		0			0
$163$	−2.32242	−	17.6405i	−0.181906	−	1.38171i	−0.802066	−	0.597236i	$-0.796266\pi$
$163$	−2.32242	−	17.6405i	−0.181906	−	1.38171i	0.620160	−	0.784475i	$-0.287068\pi$
$164$		0			0
$165$	−1.59769	−	0.210340i	−0.124380	−	0.0163749i
$166$		0			0
$167$	−8.04993	+	8.04993i	−0.622923	+	0.622923i	−0.946278	−	0.323355i	$-0.895189\pi$
$167$	−8.04993	+	8.04993i	−0.622923	+	0.622923i	0.323355	+	0.946278i	$0.395189\pi$
$168$		0			0
$169$	−4.42770	−	4.42770i	−0.340592	−	0.340592i
$170$		0			0
$171$	−2.06006	+	15.6477i	−0.157537	+	1.19661i
$172$		0			0
$173$	−11.6526	+	1.53409i	−0.885930	+	0.116635i	−0.559739	−	0.828669i	$-0.689099\pi$
$173$	−11.6526	+	1.53409i	−0.885930	+	0.116635i	−0.326191	+	0.945304i	$0.605765\pi$
$174$		0			0
$175$	2.17742	+	1.36088i	0.164598	+	0.102873i
$176$		0			0
$177$	0.651916	−	0.376384i	0.0490010	−	0.0282907i
$178$		0			0
$179$	−9.40126	−	12.2520i	−0.702683	−	0.915755i	0.296545	−	0.955019i	$-0.404165\pi$
$179$	−9.40126	−	12.2520i	−0.702683	−	0.915755i	−0.999229	+	0.0392638i	$0.987499\pi$
$180$		0			0
$181$	−8.34933	+	3.45841i	−0.620601	+	0.257061i	−0.670754	−	0.741680i	$-0.734029\pi$
$181$	−8.34933	+	3.45841i	−0.620601	+	0.257061i	0.0501528	+	0.998742i	$0.484029\pi$
$182$		0			0
$183$	−0.176757	−	0.176757i	−0.0130663	−	0.0130663i
$184$		0			0
$185$	−1.59626	−	5.95731i	−0.117359	−	0.437990i
$186$		0			0
$187$	−5.61280	+	7.31474i	−0.410448	+	0.534907i
$188$		0			0
$189$	−2.04493	−	0.932157i	−0.148747	−	0.0678044i
$190$		0			0
$191$	−2.50611	−	4.34070i	−0.181335	−	0.314082i	0.761000	−	0.648752i	$-0.224709\pi$
$191$	−2.50611	−	4.34070i	−0.181335	−	0.314082i	−0.942336	+	0.334670i	$0.891375\pi$
$192$		0			0
$193$	−1.71455	+	2.96969i	−0.123416	+	0.213763i	−0.921113	−	0.389296i	$-0.872718\pi$
$193$	−1.71455	+	2.96969i	−0.123416	+	0.213763i	0.797697	+	0.603059i	$0.206052\pi$
$194$		0			0
$195$	−1.15618	−	0.478905i	−0.0827958	−	0.0342951i
$196$		0			0
$197$	−0.277895	−	0.670899i	−0.0197992	−	0.0477995i	0.913671	−	0.406455i	$-0.133235\pi$
$197$	−0.277895	−	0.670899i	−0.0197992	−	0.0477995i	−0.933470	+	0.358656i	$0.883235\pi$
$198$		0			0
$199$	0.0187822	+	0.0700962i	0.00133144	+	0.00496898i	0.966588	−	0.256334i	$-0.0825146\pi$
$199$	0.0187822	+	0.0700962i	0.00133144	+	0.00496898i	−0.965257	+	0.261303i	$0.915848\pi$
$200$		0			0
$201$	0.408763	−	1.52552i	0.0288319	−	0.107602i
$202$		0			0
$203$	12.9499	−	4.84043i	0.908908	−	0.339732i
$204$		0			0
$205$	−23.2558	+	3.06168i	−1.62425	+	0.213837i
$206$		0			0
$207$	2.83131	+	1.63466i	0.196790	+	0.113617i
$208$		0			0
$209$			29.9332i			2.07052i
$210$		0			0
$211$	3.69703	−	8.92541i	0.254514	−	0.614451i	−0.744044	−	0.668130i	$-0.767095\pi$
$211$	3.69703	−	8.92541i	0.254514	−	0.614451i	0.998558	+	0.0536794i	$0.0170949\pi$
$212$		0			0
$213$	0.105011	−	0.797638i	0.00719524	−	0.0546533i
$214$		0			0
$215$	2.05886	−	7.68378i	0.140413	−	0.524029i
$216$		0			0
$217$	−1.37516	−	5.95898i	−0.0933522	−	0.404522i
$218$		0			0
$219$	−0.757038	+	0.986591i	−0.0511559	+	0.0666677i
$220$		0			0
$221$	−5.68048	+	4.35879i	−0.382110	+	0.293204i
$222$		0			0
$223$	12.6555			0.847474			0.423737	−	0.905785i	$-0.360718\pi$
$223$	12.6555			0.847474			0.423737	+	0.905785i	$0.360718\pi$
$224$		0			0
$225$	−2.89193			−0.192796
$226$		0			0
$227$	4.39171	−	3.36988i	0.291488	−	0.223667i	−0.452657	−	0.891685i	$-0.649524\pi$
$227$	4.39171	−	3.36988i	0.291488	−	0.223667i	0.744145	+	0.668018i	$0.232857\pi$
$228$		0			0
$229$	5.63690	−	7.34615i	0.372497	−	0.485447i	−0.569063	−	0.822294i	$-0.692694\pi$
$229$	5.63690	−	7.34615i	0.372497	−	0.485447i	0.941559	+	0.336847i	$0.109360\pi$
$230$		0			0
$231$	−2.03110	−	0.621174i	−0.133637	−	0.0408703i
$232$		0			0
$233$	−3.18027	+	11.8689i	−0.208347	+	0.777560i	0.780057	+	0.625709i	$0.215190\pi$
$233$	−3.18027	+	11.8689i	−0.208347	+	0.777560i	−0.988403	+	0.151851i	$0.951476\pi$
$234$		0			0
$235$	3.16755	−	24.0599i	0.206628	−	1.56950i
$236$		0			0
$237$	−0.126708	+	0.305901i	−0.00823060	+	0.0198704i
$238$		0			0
$239$		−	14.4049i		−	0.931776i	−0.884844	−	0.465888i	$-0.845735\pi$
$239$		−	14.4049i		−	0.931776i	0.884844	−	0.465888i	$-0.154265\pi$
$240$		0			0
$241$	−17.7988	−	10.2762i	−1.14652	−	0.661945i	−0.198485	−	0.980104i	$-0.563602\pi$
$241$	−17.7988	−	10.2762i	−1.14652	−	0.661945i	−0.948037	+	0.318159i	$0.896936\pi$
$242$		0			0
$243$	3.76846	−	0.496127i	0.241747	−	0.0318266i
$244$		0			0
$245$	−10.5223	−	9.31275i	−0.672242	−	0.594970i
$246$		0			0
$247$	−6.01638	+	22.4534i	−0.382813	+	1.42868i
$248$		0			0
$249$	−0.543306	−	2.02765i	−0.0344306	−	0.128497i
$250$		0			0
$251$	7.51258	+	18.1370i	0.474190	+	1.14480i	0.962294	+	0.272011i	$0.0876886\pi$
$251$	7.51258	+	18.1370i	0.474190	+	1.14480i	−0.488104	+	0.872785i	$0.662311\pi$
$252$		0			0
$253$	5.72853	+	2.37284i	0.360150	+	0.149179i
$254$		0			0
$255$	−0.232597	+	0.402869i	−0.0145658	+	0.0252287i
$256$		0			0
$257$	6.88465	+	11.9246i	0.429453	+	0.743834i	0.996825	−	0.0796275i	$-0.0253731\pi$
$257$	6.88465	+	11.9246i	0.429453	+	0.743834i	−0.567372	+	0.823462i	$0.692040\pi$
$258$		0			0
$259$	−0.778374	−	8.09151i	−0.0483658	−	0.502782i
$260$		0			0
$261$	−9.47881	+	12.3530i	−0.586724	+	0.764633i
$262$		0			0
$263$	−2.60568	−	9.72453i	−0.160673	−	0.599640i	−0.998553	−	0.0537847i	$-0.982872\pi$
$263$	−2.60568	−	9.72453i	−0.160673	−	0.599640i	0.837880	−	0.545855i	$-0.183795\pi$
$264$		0			0
$265$	9.38324	+	9.38324i	0.576408	+	0.576408i
$266$		0			0
$267$	−0.0517981	+	0.0214555i	−0.00316999	+	0.00131305i
$268$		0			0
$269$	7.92674	+	10.3303i	0.483302	+	0.629851i	0.969821	−	0.243819i	$-0.0784003\pi$
$269$	7.92674	+	10.3303i	0.483302	+	0.629851i	−0.486519	+	0.873670i	$0.661734\pi$
$270$		0			0
$271$	24.7118	−	14.2674i	1.50114	−	0.866682i	0.501139	−	0.865367i	$-0.332915\pi$
$271$	24.7118	−	14.2674i	1.50114	−	0.866682i	0.999999	−	0.00131542i	$-0.000418712\pi$
$272$		0			0
$273$	−1.39872	−	0.874193i	−0.0846541	−	0.0529086i
$274$		0			0
$275$	−5.43786	+	0.715907i	−0.327915	+	0.0431708i
$276$		0			0
$277$	3.24070	−	24.6156i	0.194715	−	1.47901i	−0.563020	−	0.826443i	$-0.690361\pi$
$277$	3.24070	−	24.6156i	0.194715	−	1.47901i	0.757735	−	0.652563i	$-0.226306\pi$
$278$		0			0
$279$	4.87041	+	4.87041i	0.291584	+	0.291584i
$280$		0			0
$281$	−20.7232	+	20.7232i	−1.23624	+	1.23624i	−0.274716	+	0.961525i	$0.588584\pi$
$281$	−20.7232	+	20.7232i	−1.23624	+	1.23624i	−0.961525	+	0.274716i	$0.911416\pi$
$282$		0			0
$283$	−2.55516	−	0.336393i	−0.151888	−	0.0199965i	0.0541986	−	0.998530i	$-0.482740\pi$
$283$	−2.55516	−	0.336393i	−0.151888	−	0.0199965i	−0.206087	+	0.978534i	$0.566073\pi$
$284$		0			0
$285$	0.197130	+	1.49735i	0.0116769	+	0.0886952i
$286$		0			0
$287$	−30.8973	−	1.08180i	−1.82381	−	0.0638564i
$288$		0			0
$289$	−7.16920	−	12.4174i	−0.421718	−	0.730437i
$290$		0			0
$291$	−1.52444	+	1.16975i	−0.0893643	+	0.0685717i
$292$		0			0
$293$	−9.97689	−	24.0863i	−0.582856	−	1.40714i	−0.890213	−	0.455545i	$-0.849445\pi$
$293$	−9.97689	−	24.0863i	−0.582856	−	1.40714i	0.307357	−	0.951594i	$-0.400555\pi$
$294$		0			0
$295$	−7.52201	+	7.52201i	−0.437948	+	0.437948i
$296$		0			0
$297$	4.63693	−	1.24246i	0.269062	−	0.0720950i
$298$		0			0
$299$	3.82015	+	2.93131i	0.220925	+	0.169522i
$300$		0			0
$301$	4.34880	−	9.54024i	0.250661	−	0.549890i
$302$		0			0
$303$	−0.141367	+	0.0816182i	−0.00812131	+	0.00468884i
$304$		0			0
$305$	3.05922	+	1.76624i	0.175170	+	0.101135i
$306$		0			0
$307$	2.09300	−	5.05296i	0.119454	−	0.288388i	−0.852831	−	0.522188i	$-0.825116\pi$
$307$	2.09300	−	5.05296i	0.119454	−	0.288388i	0.972285	+	0.233800i	$0.0751161\pi$
$308$		0			0
$309$	1.56932	−	0.650035i	0.0892757	−	0.0369792i
$310$		0			0
$311$	−12.0121	+	3.21864i	−0.681145	+	0.182512i	−0.582770	−	0.812637i	$-0.698031\pi$
$311$	−12.0121	+	3.21864i	−0.681145	+	0.182512i	−0.0983753	+	0.995149i	$0.531365\pi$
$312$		0			0
$313$	27.5493	+	7.38181i	1.55718	+	0.417245i	0.931769	−	0.363052i	$-0.118265\pi$
$313$	27.5493	+	7.38181i	1.55718	+	0.417245i	0.625409	+	0.780297i	$0.284932\pi$
$314$		0			0
$315$	15.6085	+	2.61344i	0.879438	+	0.147251i
$316$		0			0
$317$	0.214404	+	1.62856i	0.0120421	+	0.0914691i	0.996411	−	0.0846527i	$-0.0269781\pi$
$317$	0.214404	+	1.62856i	0.0120421	+	0.0914691i	−0.984368	+	0.176122i	$0.943645\pi$
$318$		0			0
$319$	−14.7655	+	25.5746i	−0.826708	+	1.43190i
$320$		0			0
$321$	−0.384468			−0.0214589
$322$		0			0
$323$	7.98321	+	3.30676i	0.444198	+	0.183993i
$324$		0			0
$325$	−4.22293	−	0.555959i	−0.234246	−	0.0308391i
$326$		0			0
$327$	2.37931	+	0.637534i	0.131576	+	0.0352557i
$328$		0			0
$329$	9.35438	−	30.5868i	0.515724	−	1.68630i
$330$		0			0
$331$	−7.69387	−	5.90372i	−0.422894	−	0.324498i	0.375295	−	0.926905i	$-0.377541\pi$
$331$	−7.69387	−	5.90372i	−0.422894	−	0.324498i	−0.798188	+	0.602408i	$0.794208\pi$
$332$		0			0
$333$	5.57337	+	7.26336i	0.305419	+	0.398030i
$334$		0			0
$335$			22.3184i			1.21938i
$336$		0			0
$337$			23.2125i			1.26447i	0.774778	+	0.632233i	$0.217862\pi$
$337$			23.2125i			1.26447i	−0.774778	+	0.632233i	$0.782138\pi$
$338$		0			0
$339$	0.968971	+	1.26279i	0.0526273	+	0.0685852i
$340$		0			0
$341$	10.3638	+	7.95241i	0.561230	+	0.430647i
$342$		0			0
$343$	−11.6512	−	14.3962i	−0.629106	−	0.777319i
$344$		0			0
$345$	0.302185	+	0.0809703i	0.0162691	+	0.00435929i
$346$		0			0
$347$	−11.9049	−	1.56731i	−0.639090	−	0.0841378i	−0.195984	−	0.980607i	$-0.562790\pi$
$347$	−11.9049	−	1.56731i	−0.639090	−	0.0841378i	−0.443106	+	0.896469i	$0.646123\pi$
$348$		0			0
$349$	15.6392	+	6.47795i	0.837145	+	0.346757i	0.759727	−	0.650242i	$-0.225332\pi$
$349$	15.6392	+	6.47795i	0.837145	+	0.346757i	0.0774177	+	0.996999i	$0.475332\pi$
$350$		0			0
$351$	3.72798			0.198985
$352$		0			0
$353$	5.07660	−	8.79292i	0.270200	−	0.468000i	−0.698713	−	0.715402i	$-0.746244\pi$
$353$	5.07660	−	8.79292i	0.270200	−	0.468000i	0.968913	+	0.247402i	$0.0795769\pi$
$354$		0			0
$355$	1.48396	+	11.2718i	0.0787606	+	0.598246i
$356$		0			0
$357$	−0.390046	+	0.473076i	−0.0206434	+	0.0250378i
$358$		0			0
$359$	0.555336	+	0.148802i	0.0293095	+	0.00785346i	0.273444	−	0.961888i	$-0.411837\pi$
$359$	0.555336	+	0.148802i	0.0293095	+	0.00785346i	−0.244135	+	0.969741i	$0.578504\pi$
$360$		0			0
$361$	8.74476	−	2.34315i	0.460251	−	0.123324i
$362$		0			0
$363$	2.74796	−	1.13824i	0.144231	−	0.0597422i
$364$		0			0
$365$	6.72509	−	16.2358i	0.352007	−	0.849821i
$366$		0			0
$367$	−6.21293	−	3.58704i	−0.324312	−	0.187242i	0.329001	−	0.944330i	$-0.393288\pi$
$367$	−6.21293	−	3.58704i	−0.324312	−	0.187242i	−0.653313	+	0.757088i	$0.726621\pi$
$368$		0			0
$369$	30.1549	−	17.4099i	1.56980	−	0.906326i
$370$		0			0
$371$	10.1552	+	14.2399i	0.527233	+	0.739297i
$372$		0			0
$373$	17.5545	+	13.4701i	0.908938	+	0.697453i	0.953448	−	0.301556i	$-0.0975061\pi$
$373$	17.5545	+	13.4701i	0.908938	+	0.697453i	−0.0445102	+	0.999009i	$0.514173\pi$
$374$		0			0
$375$	−1.64444	+	0.440626i	−0.0849184	+	0.0227538i
$376$		0			0
$377$	−16.2162	+	16.2162i	−0.835176	+	0.835176i
$378$		0			0
$379$	−8.55798	−	20.6608i	−0.439594	−	1.06127i	−0.976089	−	0.217370i	$-0.930252\pi$
$379$	−8.55798	−	20.6608i	−0.439594	−	1.06127i	0.536495	−	0.843903i	$-0.319748\pi$
$380$		0			0
$381$	−1.00065	+	0.767823i	−0.0512647	+	0.0393368i
$382$		0			0
$383$	−8.59870	−	14.8934i	−0.439373	−	0.761016i	0.558268	−	0.829660i	$-0.311466\pi$
$383$	−8.59870	−	14.8934i	−0.439373	−	0.761016i	−0.997641	+	0.0686443i	$0.978133\pi$
$384$		0			0
$385$	29.9964	+	1.05026i	1.52876	+	0.0535260i
$386$		0			0
$387$	1.54132	+	11.7075i	0.0783499	+	0.595126i
$388$		0			0
$389$	−27.7279	−	3.65045i	−1.40586	−	0.185085i	−0.610882	−	0.791721i	$-0.709185\pi$
$389$	−27.7279	−	3.65045i	−1.40586	−	0.185085i	−0.794980	+	0.606636i	$0.792519\pi$
$390$		0			0
$391$	1.26568	−	1.26568i	0.0640080	−	0.0640080i
$392$		0			0
$393$	−0.318314	−	0.318314i	−0.0160568	−	0.0160568i
$394$		0			0
$395$	0.610733	−	4.63898i	0.0307293	−	0.233412i
$396$		0			0
$397$	−6.47546	+	0.852511i	−0.324994	+	0.0427863i	−0.291258	−	0.956644i	$-0.594074\pi$
$397$	−6.47546	+	0.852511i	−0.324994	+	0.0427863i	−0.0337360	+	0.999431i	$0.510741\pi$
$398$		0			0
$399$	−0.0696526	+	1.98935i	−0.00348699	+	0.0995922i
$400$		0			0
$401$	12.7049	−	7.33520i	0.634454	−	0.366302i	−0.148021	−	0.988984i	$-0.547290\pi$
$401$	12.7049	−	7.33520i	0.634454	−	0.366302i	0.782475	+	0.622682i	$0.213957\pi$
$402$		0			0
$403$	6.17568	+	8.04830i	0.307632	+	0.400914i
$404$		0			0
$405$	−16.3550	+	6.77446i	−0.812686	+	0.336626i
$406$		0			0
$407$	12.2780	+	12.2780i	0.608597	+	0.608597i
$408$		0			0
$409$	−0.870878	−	3.25016i	−0.0430621	−	0.160710i	0.941047	−	0.338277i	$-0.109844\pi$
$409$	−0.870878	−	3.25016i	−0.0430621	−	0.160710i	−0.984109	+	0.177567i	$0.943177\pi$
$410$		0			0
$411$	0.791025	−	1.03088i	0.0390184	−	0.0508497i
$412$		0			0
$413$	−11.4153	+	8.14086i	−0.561710	+	0.400586i
$414$		0			0
$415$	14.8322	+	25.6902i	0.728085	+	1.26108i
$416$		0			0
$417$	−0.303110	+	0.525002i	−0.0148434	+	0.0257095i
$418$		0			0
$419$	4.39323	+	1.81973i	0.214623	+	0.0888998i	0.487405	−	0.873176i	$-0.337944\pi$
$419$	4.39323	+	1.81973i	0.214623	+	0.0888998i	−0.272782	+	0.962076i	$0.587944\pi$
$420$		0			0
$421$	−10.8928	−	26.2977i	−0.530885	−	1.28167i	−0.930938	−	0.365177i	$-0.881008\pi$
$421$	−10.8928	−	26.2977i	−0.530885	−	1.28167i	0.400053	−	0.916492i	$-0.368992\pi$
$422$		0			0
$423$	9.32367	+	34.7964i	0.453332	+	1.69186i
$424$		0			0
$425$	−0.409794	+	1.52937i	−0.0198779	+	0.0741854i
$426$		0			0
$427$	3.59234	+	2.96185i	0.173845	+	0.143334i
$428$		0			0
$429$	3.49313	−	0.459879i	0.168650	−	0.0222032i
$430$		0			0
$431$	9.18556	+	5.30328i	0.442453	+	0.255450i	0.704637	−	0.709567i	$-0.251110\pi$
$431$	9.18556	+	5.30328i	0.442453	+	0.255450i	−0.262185	+	0.965018i	$0.584443\pi$
$432$		0			0
$433$		−	6.85711i		−	0.329532i	−0.986333	−	0.164766i	$-0.947313\pi$
$433$		−	6.85711i		−	0.329532i	0.986333	−	0.164766i	$-0.0526869\pi$
$434$		0			0
$435$	−0.570189	+	1.37656i	−0.0273385	+	0.0660009i
$436$		0			0
$437$	0.758501	−	5.76139i	0.0362840	−	0.275604i
$438$		0			0
$439$	8.57905	−	32.0175i	0.409456	−	1.52811i	−0.386231	−	0.922402i	$-0.626223\pi$
$439$	8.57905	−	32.0175i	0.409456	−	1.52811i	0.795687	−	0.605708i	$-0.207110\pi$
$440$		0			0
$441$	19.7211	+	6.79457i	0.939100	+	0.323551i
$442$		0			0
$443$	1.91439	−	2.49488i	0.0909553	−	0.118535i	−0.745659	−	0.666328i	$-0.767865\pi$
$443$	1.91439	−	2.49488i	0.0909553	−	0.118535i	0.836614	+	0.547793i	$0.184532\pi$
$444$		0			0
$445$	0.628569	−	0.482318i	0.0297970	−	0.0228641i
$446$		0			0
$447$	−1.98512			−0.0938930
$448$		0			0
$449$	−11.3473			−0.535514			−0.267757	−	0.963486i	$-0.586282\pi$
$449$	−11.3473			−0.535514			−0.267757	+	0.963486i	$0.586282\pi$
$450$		0			0
$451$	52.3920	−	40.2018i	2.46704	−	1.89303i
$452$		0			0
$453$	0.183687	−	0.239386i	0.00863039	−	0.0112473i
$454$		0			0
$455$	22.2898	+	6.81691i	1.04496	+	0.319582i
$456$		0			0
$457$	−5.90491	+	22.0374i	−0.276220	+	1.03087i	0.678799	+	0.734324i	$0.262501\pi$
$457$	−5.90491	+	22.0374i	−0.276220	+	1.03087i	−0.955019	+	0.296544i	$0.904166\pi$
$458$		0			0
$459$	0.180882	−	1.37393i	0.00844283	−	0.0641296i
$460$		0			0
$461$	13.5684	−	32.7570i	0.631943	−	1.52565i	−0.205234	−	0.978713i	$-0.565796\pi$
$461$	13.5684	−	32.7570i	0.631943	−	1.52565i	0.837177	−	0.546932i	$-0.184204\pi$
$462$		0			0
$463$			1.58276i			0.0735570i	0.999323	+	0.0367785i	$0.0117096\pi$
$463$			1.58276i			0.0735570i	−0.999323	+	0.0367785i	$0.988290\pi$
$464$		0			0
$465$	0.570799	+	0.329551i	0.0264702	+	0.0152826i
$466$		0			0
$467$	−39.2952	+	5.17331i	−1.81836	+	0.239392i	−0.961239	−	0.275717i	$-0.911085\pi$
$467$	−39.2952	+	5.17331i	−1.81836	+	0.239392i	−0.857124	+	0.515109i	$0.827751\pi$
$468$		0			0
$469$	−4.85774	+	29.0123i	−0.224310	+	1.33967i
$470$		0			0
$471$	0.0527752	−	0.196960i	0.00243175	−	0.00907543i
$472$		0			0
$473$	5.79646	+	21.6327i	0.266522	+	0.994673i
$474$		0			0
$475$	1.96711	+	4.74903i	0.0902573	+	0.217900i
$476$		0			0
$477$	−18.1990	−	7.53829i	−0.833276	−	0.345154i
$478$		0			0
$479$	−13.8202	+	23.9373i	−0.631460	+	1.09372i	0.355793	+	0.934565i	$0.384211\pi$
$479$	−13.8202	+	23.9373i	−0.631460	+	1.09372i	−0.987253	+	0.159157i	$0.949122\pi$
$480$		0			0
$481$	6.74215	+	11.6777i	0.307415	+	0.532459i
$482$		0			0
$483$	0.375196	+	0.171028i	0.0170720	+	0.00778205i
$484$		0			0
$485$	16.5302	−	21.5426i	0.750600	−	0.978200i
$486$		0			0
$487$	−6.15641	−	22.9760i	−0.278974	−	1.04114i	−0.953131	−	0.302556i	$-0.902160\pi$
$487$	−6.15641	−	22.9760i	−0.278974	−	1.04114i	0.674158	−	0.738587i	$-0.264507\pi$
$488$		0			0
$489$	1.78717	+	1.78717i	0.0808184	+	0.0808184i
$490$		0			0
$491$	−15.1411	+	6.27166i	−0.683309	+	0.283036i	−0.697210	−	0.716867i	$-0.745575\pi$
$491$	−15.1411	+	6.27166i	−0.683309	+	0.283036i	0.0139002	+	0.999903i	$0.495575\pi$
$492$		0			0
$493$	5.18961	+	6.76323i	0.233728	+	0.304600i
$494$		0			0
$495$	−29.2757	+	16.9023i	−1.31585	+	0.759704i
$496$		0			0
$497$	−0.524335	+	14.9756i	−0.0235196	+	0.671746i
$498$		0			0
$499$	21.1492	−	2.78435i	0.946769	−	0.124645i	0.358698	−	0.933454i	$-0.383221\pi$
$499$	21.1492	−	2.78435i	0.946769	−	0.124645i	0.588071	+	0.808809i	$0.299887\pi$
$500$		0			0
$501$	0.211078	−	1.60329i	0.00943026	−	0.0716299i
$502$		0			0
$503$	−18.8318	−	18.8318i	−0.839666	−	0.839666i	0.149149	−	0.988815i	$-0.452347\pi$
$503$	−18.8318	−	18.8318i	−0.839666	−	0.839666i	−0.988815	+	0.149149i	$0.952347\pi$
$504$		0			0
$505$	1.63113	−	1.63113i	0.0725845	−	0.0725845i
$506$		0			0
$507$	0.881858	+	0.116099i	0.0391647	+	0.00515613i
$508$		0			0
$509$	−3.96554	−	30.1213i	−0.175769	−	1.33510i	−0.820919	−	0.571045i	$-0.806538\pi$
$509$	−3.96554	−	30.1213i	−0.175769	−	1.33510i	0.645149	−	0.764056i	$-0.276795\pi$
$510$		0			0
$511$	12.2760	−	19.6416i	0.543057	−	0.868895i
$512$		0			0
$513$	−2.24951	−	3.89626i	−0.0993181	−	0.172024i
$514$		0			0
$515$	−19.0437	+	14.6128i	−0.839167	+	0.643915i
$516$		0			0
$517$	26.1458	+	63.1214i	1.14989	+	2.77608i
$518$		0			0
$519$	1.18053	−	1.18053i	0.0518194	−	0.0518194i
$520$		0			0
$521$	−8.16141	+	2.18684i	−0.357558	+	0.0958073i	−0.433126	−	0.901333i	$-0.642590\pi$
$521$	−8.16141	+	2.18684i	−0.357558	+	0.0958073i	0.0755684	+	0.997141i	$0.475923\pi$
$522$		0			0
$523$	20.4005	+	15.6538i	0.892051	+	0.684495i	0.949471	−	0.313855i	$-0.101621\pi$
$523$	20.4005	+	15.6538i	0.892051	+	0.684495i	−0.0574200	+	0.998350i	$0.518287\pi$
$524$		0			0
$525$	−0.363065	+	0.0349255i	−0.0158454	+	0.00152427i
$526$		0			0
$527$	3.26582	−	1.88552i	0.142261	−	0.0821345i
$528$		0			0
$529$	18.8761	+	10.8981i	0.820701	+	0.473832i
$530$		0			0
$531$	6.04301	−	14.5891i	0.262244	−	0.633114i
$532$		0			0
$533$	47.3805	−	19.6257i	2.05228	−	0.850081i
$534$		0			0
$535$	5.24797	−	1.40619i	0.226890	−	0.0607949i
$536$		0			0
$537$	2.11895	+	0.567770i	0.0914393	+	0.0245011i
$538$		0			0
$539$	38.7646	+	7.89417i	1.66971	+	0.340026i
$540$		0			0
$541$	−4.09000	−	31.0667i	−0.175843	−	1.33566i	−0.820701	−	0.571358i	$-0.806417\pi$
$541$	−4.09000	−	31.0667i	−0.175843	−	1.33566i	0.644858	−	0.764302i	$-0.276916\pi$
$542$		0			0
$543$	0.641865	−	1.11174i	0.0275451	−	0.0477094i
$544$		0			0
$545$	−34.8093			−1.49106
$546$		0			0
$547$	13.4950	+	5.58982i	0.577005	+	0.239003i	0.652049	−	0.758177i	$-0.273910\pi$
$547$	13.4950	+	5.58982i	0.577005	+	0.239003i	−0.0750437	+	0.997180i	$0.523910\pi$
$548$		0			0
$549$	−5.19893	−	0.684452i	−0.221885	−	0.0292117i
$550$		0			0
$551$	26.7332	+	7.16315i	1.13887	+	0.305160i
$552$		0			0
$553$	1.80361	−	5.89741i	0.0766974	−	0.250784i
$554$		0			0
$555$	0.695040	+	0.533323i	0.0295028	+	0.0226383i
$556$		0			0
$557$	1.41794	+	1.84790i	0.0600801	+	0.0782979i	0.822427	−	0.568871i	$-0.192620\pi$
$557$	1.41794	+	1.84790i	0.0600801	+	0.0782979i	−0.762347	+	0.647169i	$0.775953\pi$
$558$		0			0
$559$			17.3921i			0.735609i
$560$		0			0
$561$		−	1.30969i		−	0.0552953i
$562$		0			0
$563$	7.77161	+	10.1282i	0.327534	+	0.426851i	0.927874	−	0.372894i	$-0.121635\pi$
$563$	7.77161	+	10.1282i	0.327534	+	0.426851i	−0.600339	+	0.799745i	$0.704968\pi$
$564$		0			0
$565$	−17.8451	−	13.6930i	−0.750748	−	0.576069i
$566$		0			0
$567$	−22.7348	+	5.24655i	−0.954774	+	0.220335i
$568$		0			0
$569$	0.794662	+	0.212929i	0.0333140	+	0.00892645i	0.275438	−	0.961319i	$-0.411177\pi$
$569$	0.794662	+	0.212929i	0.0333140	+	0.00892645i	−0.242124	+	0.970245i	$0.577844\pi$
$570$		0			0
$571$	−8.56765	−	1.12795i	−0.358545	−	0.0472034i	−0.0508979	−	0.998704i	$-0.516208\pi$
$571$	−8.56765	−	1.12795i	−0.358545	−	0.0472034i	−0.307647	+	0.951501i	$0.599542\pi$
$572$		0			0
$573$	0.657782	+	0.272462i	0.0274792	+	0.0113823i
$574$		0			0
$575$	1.06479			0.0444049
$576$		0			0
$577$	−6.56242	+	11.3664i	−0.273197	+	0.473191i	−0.969679	−	0.244384i	$-0.921414\pi$
$577$	−6.56242	+	11.3664i	−0.273197	+	0.473191i	0.696482	+	0.717575i	$0.254748\pi$
$578$		0			0
$579$	−0.0635792	−	0.482932i	−0.00264226	−	0.0200700i
$580$		0			0
$581$	13.6892	+	36.6237i	0.567925	+	1.51941i
$582$		0			0
$583$	−36.0867	−	9.66941i	−1.49456	−	0.400466i
$584$		0			0
$585$	−25.3575	+	6.79453i	−1.04840	+	0.280919i
$586$		0			0
$587$	7.38530	−	3.05909i	0.304824	−	0.126262i	−0.225028	−	0.974352i	$-0.572247\pi$
$587$	7.38530	−	3.05909i	0.304824	−	0.126262i	0.529852	+	0.848090i	$0.322247\pi$
$588$		0			0
$589$	4.68513	−	11.3109i	0.193047	−	0.466057i
$590$		0			0
$591$	0.0893325	+	0.0515761i	0.00367465	+	0.00212156i
$592$		0			0
$593$	−34.8928	+	20.1454i	−1.43288	+	0.827272i	−0.997339	−	0.0728986i	$-0.976775\pi$
$593$	−34.8928	+	20.1454i	−1.43288	+	0.827272i	−0.435538	+	0.900171i	$0.643442\pi$
$594$		0			0
$595$	3.59385	−	7.88406i	0.147333	−	0.323215i
$596$		0			0
$597$	−0.00817814	−	0.00627531i	−0.000334709	−	0.000256831i
$598$		0			0
$599$	−15.8283	+	4.24117i	−0.646726	+	0.173290i	−0.567248	−	0.823547i	$-0.691992\pi$
$599$	−15.8283	+	4.24117i	−0.646726	+	0.173290i	−0.0794778	+	0.996837i	$0.525325\pi$
$600$		0			0
$601$	31.9538	−	31.9538i	1.30342	−	1.30342i	0.377353	−	0.926070i	$-0.376834\pi$
$601$	31.9538	−	31.9538i	1.30342	−	1.30342i	0.926070	−	0.377353i	$-0.123166\pi$
$602$		0			0
$603$	−12.6785	−	30.6086i	−0.516308	−	1.24648i
$604$		0			0
$605$	−33.3465	+	25.5876i	−1.35573	+	1.04029i
$606$		0			0
$607$	−2.68994	−	4.65912i	−0.109181	−	0.189108i	0.806257	−	0.591565i	$-0.201490\pi$
$607$	−2.68994	−	4.65912i	−0.109181	−	0.189108i	−0.915439	+	0.402457i	$0.868156\pi$
$608$		0			0
$609$	−1.04082	+	1.66532i	−0.0421762	+	0.0674823i
$610$		0			0
$611$	6.92541	+	52.6037i	0.280172	+	2.12812i
$612$		0			0
$613$	13.8223	+	1.81973i	0.558276	+	0.0734984i	0.404384	−	0.914589i	$-0.367486\pi$
$613$	13.8223	+	1.81973i	0.558276	+	0.0734984i	0.153892	+	0.988088i	$0.450819\pi$
$614$		0			0
$615$	2.35605	−	2.35605i	0.0950051	−	0.0950051i
$616$		0			0
$617$	29.4145	+	29.4145i	1.18418	+	1.18418i	0.978651	+	0.205531i	$0.0658920\pi$
$617$	29.4145	+	29.4145i	1.18418	+	1.18418i	0.205531	+	0.978651i	$0.434108\pi$
$618$		0			0
$619$	1.46506	−	11.1282i	0.0588858	−	0.447282i	−0.936449	−	0.350803i	$-0.885909\pi$
$619$	1.46506	−	11.1282i	0.0588858	−	0.447282i	0.995335	−	0.0964787i	$-0.0307580\pi$
$620$		0			0
$621$	−0.923977	+	0.121644i	−0.0370779	+	0.00488140i
$622$		0			0
$623$	0.922075	−	0.490167i	0.0369422	−	0.0196381i
$624$		0			0
$625$	16.6325	−	9.60280i	0.665301	−	0.384112i
$626$		0			0
$627$	−2.58844	−	3.37331i	−0.103372	−	0.134717i
$628$		0			0
$629$	4.63092	−	1.91819i	0.184647	−	0.0764832i
$630$		0			0
$631$	24.4532	+	24.4532i	0.973465	+	0.973465i	0.999657	−	0.0261920i	$-0.00833811\pi$
$631$	24.4532	+	24.4532i	0.973465	+	0.973465i	−0.0261920	+	0.999657i	$0.508338\pi$
$632$		0			0
$633$	0.355178	+	1.32554i	0.0141171	+	0.0526856i
$634$		0			0
$635$	10.8505	−	14.1406i	0.430588	−	0.561154i
$636$		0			0
$637$	27.4914	+	13.7130i	1.08925	+	0.543329i
$638$		0			0
$639$	−8.43841	−	14.6157i	−0.333818	−	0.578190i
$640$		0			0
$641$	−1.75650	+	3.04235i	−0.0693777	+	0.120166i	−0.898628	−	0.438712i	$-0.855435\pi$
$641$	−1.75650	+	3.04235i	−0.0693777	+	0.120166i	0.829250	+	0.558878i	$0.188768\pi$
$642$		0			0
$643$	−36.1599	−	14.9779i	−1.42601	−	0.590672i	−0.469645	−	0.882855i	$-0.655618\pi$
$643$	−36.1599	−	14.9779i	−1.42601	−	0.590672i	−0.956362	+	0.292183i	$0.905618\pi$
$644$		0			0
$645$	0.432422	+	1.04396i	0.0170266	+	0.0411059i
$646$		0			0
$647$	7.08897	+	26.4564i	0.278696	+	1.04011i	0.953324	+	0.301950i	$0.0976377\pi$
$647$	7.08897	+	26.4564i	0.278696	+	1.04011i	−0.674627	+	0.738158i	$0.735696\pi$
$648$		0			0
$649$	7.75141	−	28.9287i	0.304270	−	1.13555i
$650$		0			0
$651$	0.670270	+	0.552631i	0.0262699	+	0.0216593i
$652$		0			0
$653$	19.6595	−	2.58823i	0.769337	−	0.101285i	0.264367	−	0.964422i	$-0.414837\pi$
$653$	19.6595	−	2.58823i	0.769337	−	0.101285i	0.504970	+	0.863137i	$0.331504\pi$
$654$		0			0
$655$	5.50921	+	3.18075i	0.215263	+	0.124282i
$656$		0			0
$657$			26.0870i			1.01775i
$658$		0			0
$659$	8.71190	−	21.0324i	0.339368	−	0.819306i	−0.658409	−	0.752660i	$-0.728770\pi$
$659$	8.71190	−	21.0324i	0.339368	−	0.819306i	0.997777	−	0.0666456i	$-0.0212297\pi$
$660$		0			0
$661$	2.00406	−	15.2224i	0.0779490	−	0.592082i	−0.907240	−	0.420612i	$-0.861815\pi$
$661$	2.00406	−	15.2224i	0.0779490	−	0.592082i	0.985189	−	0.171469i	$-0.0548514\pi$
$662$		0			0
$663$	0.263240	−	0.982425i	0.0102234	−	0.0381542i
$664$		0			0
$665$	−6.32530	−	27.4094i	−0.245285	−	1.06289i
$666$		0			0
$667$	3.49004	−	4.54831i	0.135135	−	0.176111i
$668$		0			0
$669$	−1.42621	+	1.09437i	−0.0551404	+	0.0423107i
$670$		0			0
$671$	−9.94526			−0.383932
$672$		0			0
$673$	−39.5412			−1.52420			−0.762101	−	0.647458i	$-0.775832\pi$
$673$	−39.5412			−1.52420			−0.762101	+	0.647458i	$0.775832\pi$
$674$		0			0
$675$	0.654019	−	0.501846i	0.0251732	−	0.0193161i
$676$		0			0
$677$	−15.2828	+	19.9169i	−0.587365	+	0.765470i	−0.988610	−	0.150502i	$-0.951911\pi$
$677$	−15.2828	+	19.9169i	−0.587365	+	0.765470i	0.401244	+	0.915971i	$0.368578\pi$
$678$		0			0
$679$	26.1770	−	24.4060i	1.00458	−	0.936616i
$680$		0			0
$681$	−0.203517	+	0.759536i	−0.00779879	+	0.0291055i
$682$		0			0
$683$	−1.45143	+	11.0247i	−0.0555375	+	0.421849i	0.940980	+	0.338463i	$0.109907\pi$
$683$	−1.45143	+	11.0247i	−0.0555375	+	0.421849i	−0.996517	+	0.0833863i	$0.973426\pi$
$684$		0			0
$685$	−7.02701	+	16.9647i	−0.268488	+	0.648188i
$686$		0			0
$687$			1.31532i			0.0501825i
$688$		0			0
$689$	−25.1258	−	14.5064i	−0.957218	−	0.552650i
$690$		0			0
$691$	14.2106	−	1.87086i	0.540596	−	0.0711708i	0.144716	−	0.989473i	$-0.453773\pi$
$691$	14.2106	−	1.87086i	0.540596	−	0.0711708i	0.395880	+	0.918302i	$0.370440\pi$
$692$		0			0
$693$	−41.7353	+	15.5998i	−1.58539	+	0.592588i
$694$		0			0
$695$	2.21725	−	8.27489i	0.0841050	−	0.313884i
$696$		0			0
$697$	−4.93406	−	18.4142i	−0.186891	−	0.697486i
$698$		0			0
$699$	−0.667952	−	1.61258i	−0.0252643	−	0.0609933i
$700$		0			0
$701$	−16.8083	−	6.96224i	−0.634842	−	0.262960i	0.0419666	−	0.999119i	$-0.486638\pi$
$701$	−16.8083	−	6.96224i	−0.634842	−	0.262960i	−0.676809	+	0.736159i	$0.736638\pi$
$702$		0			0
$703$	8.13659	−	14.0930i	0.306877	−	0.531527i
$704$		0			0
$705$	1.72359	+	2.98534i	0.0649140	+	0.112434i
$706$		0			0
$707$	2.47539	−	1.76533i	0.0930965	−	0.0663922i
$708$		0			0
$709$	−13.6778	+	17.8253i	−0.513682	+	0.669443i	−0.976126	−	0.217205i	$-0.930306\pi$
$709$	−13.6778	+	17.8253i	−0.513682	+	0.669443i	0.462444	+	0.886648i	$0.346973\pi$
$710$		0			0
$711$	1.79769	+	6.70907i	0.0674187	+	0.251610i
$712$		0			0
$713$	−1.79325	−	1.79325i	−0.0671579	−	0.0671579i
$714$		0			0
$715$	−45.9991	+	19.0535i	−1.72027	+	0.712559i
$716$		0			0
$717$	1.24565	+	1.62336i	0.0465195	+	0.0606254i
$718$		0			0
$719$	28.3611	−	16.3743i	1.05769	−	0.610658i	0.132898	−	0.991130i	$-0.457572\pi$
$719$	28.3611	−	16.3743i	1.05769	−	0.610658i	0.924792	+	0.380472i	$0.124238\pi$
$720$		0			0
$721$	−27.9361	+	14.8506i	−1.04039	+	0.553064i
$722$		0			0
$723$	2.89445	−	0.381062i	0.107646	−	0.0141718i
$724$		0			0
$725$	−0.661930	+	5.02786i	−0.0245835	+	0.186730i
$726$		0			0
$727$	−7.89885	−	7.89885i	−0.292952	−	0.292952i	0.545293	−	0.838245i	$-0.316418\pi$
$727$	−7.89885	−	7.89885i	−0.292952	−	0.292952i	−0.838245	+	0.545293i	$0.816418\pi$
$728$		0			0
$729$	18.3257	−	18.3257i	0.678731	−	0.678731i
$730$		0			0
$731$	6.40981	+	0.843868i	0.237075	+	0.0312116i
$732$		0			0
$733$	−3.78735	−	28.7678i	−0.139889	−	1.06256i	−0.907025	−	0.421077i	$-0.861652\pi$
$733$	−3.78735	−	28.7678i	−0.139889	−	1.06256i	0.767136	−	0.641484i	$-0.221681\pi$
$734$		0			0
$735$	1.99111	+	0.139600i	0.0734433	+	0.00514921i
$736$		0			0
$737$	−31.4173	−	54.4164i	−1.15727	−	2.00445i
$738$		0			0
$739$	−0.0470417	+	0.0360963i	−0.00173046	+	0.00132782i	−0.609626	−	0.792689i	$-0.708680\pi$
$739$	−0.0470417	+	0.0360963i	−0.00173046	+	0.00132782i	0.607896	+	0.794017i	$0.292014\pi$
$740$		0			0
$741$	−1.26362	−	3.05064i	−0.0464202	−	0.112068i
$742$		0			0
$743$	17.5570	−	17.5570i	0.644103	−	0.644103i	−0.307459	−	0.951561i	$-0.599479\pi$
$743$	17.5570	−	17.5570i	0.644103	−	0.644103i	0.951561	+	0.307459i	$0.0994785\pi$
$744$		0			0
$745$	27.0968	−	7.26058i	0.992751	−	0.266007i
$746$		0			0
$747$	−34.9356	−	26.8070i	−1.27823	−	0.980818i
$748$		0			0
$749$	7.12806	−	0.685694i	0.260454	−	0.0250547i
$750$		0			0
$751$	−11.9336	+	6.88986i	−0.435463	+	0.251415i	−0.701671	−	0.712501i	$-0.747562\pi$
$751$	−11.9336	+	6.88986i	−0.435463	+	0.251415i	0.266208	+	0.963916i	$0.414229\pi$
$752$		0			0
$753$	−2.41500	−	1.39430i	−0.0880076	−	0.0508112i
$754$		0			0
$755$	−1.63177	+	3.93945i	−0.0593863	+	0.143371i
$756$		0			0
$757$	−8.12594	+	3.36587i	−0.295342	+	0.122335i	−0.525434	−	0.850834i	$-0.676097\pi$
$757$	−8.12594	+	3.36587i	−0.295342	+	0.122335i	0.230092	+	0.973169i	$0.426097\pi$
$758$		0			0
$759$	−0.850764	+	0.227962i	−0.0308808	+	0.00827448i
$760$		0			0
$761$	9.95345	+	2.66702i	0.360812	+	0.0966793i	0.434671	−	0.900589i	$-0.356865\pi$
$761$	9.95345	+	2.66702i	0.360812	+	0.0966793i	−0.0738587	+	0.997269i	$0.523531\pi$
$762$		0			0
$763$	−45.2496	−	7.57645i	−1.63814	−	0.274286i
$764$		0			0
$765$	1.27375	+	9.67509i	0.0460525	+	0.349804i
$766$		0			0
$767$	11.6290	−	20.1419i	0.419897	−	0.727284i
$768$		0			0
$769$	21.6646			0.781244			0.390622	−	0.920551i	$-0.372260\pi$
$769$	21.6646			0.781244			0.390622	+	0.920551i	$0.372260\pi$
$770$		0			0
$771$	−1.80703	−	0.748495i	−0.0650785	−	0.0269564i
$772$		0			0
$773$	5.86102	+	0.771618i	0.210806	+	0.0277532i	0.235190	−	0.971950i	$-0.424429\pi$
$773$	5.86102	+	0.771618i	0.210806	+	0.0277532i	−0.0243834	+	0.999703i	$0.507762\pi$
$774$		0			0
$775$	2.16686	+	0.580610i	0.0778361	+	0.0208561i
$776$		0			0
$777$	0.787422	+	0.844562i	0.0282486	+	0.0302985i
$778$		0			0
$779$	−49.1016	−	37.6769i	−1.75925	−	1.34992i
$780$		0			0
$781$	−19.4854	−	25.3938i	−0.697241	−	0.908662i
$782$		0			0
$783$		−	4.43856i		−	0.158621i
$784$		0			0
$785$			2.88152i			0.102846i
$786$		0			0
$787$	−1.22092	−	1.59113i	−0.0435210	−	0.0567177i	0.771086	−	0.636731i	$-0.219714\pi$
$787$	−1.22092	−	1.59113i	−0.0435210	−	0.0567177i	−0.814607	+	0.580014i	$0.803047\pi$
$788$		0			0
$789$	1.13456	+	0.870581i	0.0403915	+	0.0309935i
$790$		0			0
$791$	−20.2170	−	21.6840i	−0.718832	−	0.770995i
$792$		0			0
$793$	−7.46012	−	1.99893i	−0.264917	−	0.0709842i
$794$		0			0
$795$	−1.86885	−	0.246038i	−0.0662812	−	0.00872608i
$796$		0			0
$797$	16.0929	+	6.66591i	0.570041	+	0.236119i	0.649038	−	0.760756i	$-0.275172\pi$
$797$	16.0929	+	6.66591i	0.570041	+	0.236119i	−0.0789969	+	0.996875i	$0.525172\pi$
$798$		0			0
$799$	19.7229			0.697747
$800$		0			0
$801$	−0.588060	+	1.01855i	−0.0207781	+	0.0359887i
$802$		0			0
$803$	6.45791	+	49.0527i	0.227895	+	1.73103i
$804$		0			0
$805$	−5.74695	−	0.962251i	−0.202553	−	0.0339149i
$806$		0			0
$807$	−1.78660	−	0.478719i	−0.0628914	−	0.0168517i
$808$		0			0
$809$	3.07372	−	0.823601i	0.108066	−	0.0289563i	−0.204381	−	0.978891i	$-0.565518\pi$
$809$	3.07372	−	0.823601i	0.108066	−	0.0289563i	0.312447	+	0.949935i	$0.398851\pi$
$810$		0			0
$811$	−11.5445	+	4.78190i	−0.405383	+	0.167915i	−0.576052	−	0.817413i	$-0.695407\pi$
$811$	−11.5445	+	4.78190i	−0.405383	+	0.167915i	0.170669	+	0.985328i	$0.445407\pi$
$812$		0			0
$813$	−1.55114	+	3.74479i	−0.0544009	+	0.131335i
$814$		0			0
$815$	−30.9313	−	17.8582i	−1.08348	−	0.625546i
$816$		0			0
$817$	18.1772	−	10.4946i	0.635941	−	0.367161i
$818$		0			0
$819$	−34.4419	+	3.31318i	−1.20350	+	0.115772i
$820$		0			0
$821$	−3.86140	−	2.96295i	−0.134764	−	0.103408i	0.539180	−	0.842191i	$-0.318734\pi$
$821$	−3.86140	−	2.96295i	−0.134764	−	0.103408i	−0.673944	+	0.738783i	$0.735401\pi$
$822$		0			0
$823$	48.9725	−	13.1222i	1.70708	−	0.457410i	0.732371	−	0.680906i	$-0.238414\pi$
$823$	48.9725	−	13.1222i	1.70708	−	0.457410i	0.974705	+	0.223496i	$0.0717471\pi$
$824$		0			0
$825$	0.550911	−	0.550911i	0.0191803	−	0.0191803i
$826$		0			0
$827$	13.4592	+	32.4934i	0.468022	+	1.12990i	0.965025	+	0.262156i	$0.0844336\pi$
$827$	13.4592	+	32.4934i	0.468022	+	1.12990i	−0.497004	+	0.867748i	$0.665566\pi$
$828$		0			0
$829$	−31.6047	+	24.2511i	−1.09768	+	0.842276i	−0.988421	−	0.151738i	$-0.951513\pi$
$829$	−31.6047	+	24.2511i	−1.09768	+	0.842276i	−0.109255	+	0.994014i	$0.534846\pi$
$830$		0			0
$831$	1.76339	+	3.05428i	0.0611714	+	0.105952i
$832$		0			0
$833$	6.38776	−	9.46650i	0.221323	−	0.327995i
$834$		0			0
$835$	2.98284	+	22.6569i	0.103226	+	0.784076i
$836$		0			0
$837$	−1.94663	−	0.256279i	−0.0672855	−	0.00885831i
$838$		0			0
$839$	38.1779	−	38.1779i	1.31805	−	1.31805i	0.402726	−	0.915321i	$-0.368063\pi$
$839$	38.1779	−	38.1779i	1.31805	−	1.31805i	0.915321	−	0.402726i	$-0.131937\pi$
$840$		0			0
$841$	−1.19897	−	1.19897i	−0.0413438	−	0.0413438i
$842$		0			0
$843$	0.543383	−	4.12741i	0.0187151	−	0.142155i
$844$		0			0
$845$	−12.4620	+	1.64065i	−0.428705	+	0.0564401i
$846$		0			0
$847$	−48.9174	+	26.0041i	−1.68082	+	0.893510i
$848$		0			0
$849$	0.317042	−	0.183044i	0.0108809	−	0.00628206i
$850$		0			0
$851$	−2.05208	−	2.67433i	−0.0703445	−	0.0916747i
$852$		0			0
$853$	−8.95318	+	3.70853i	−0.306551	+	0.126978i	−0.530656	−	0.847587i	$-0.678054\pi$
$853$	−8.95318	+	3.70853i	−0.306551	+	0.126978i	0.224105	+	0.974565i	$0.428054\pi$
$854$		0			0
$855$	22.4023	+	22.4023i	0.766142	+	0.766142i
$856$		0			0
$857$	−0.321965	−	1.20159i	−0.0109981	−	0.0410455i	0.960209	−	0.279283i	$-0.0900969\pi$
$857$	−0.321965	−	1.20159i	−0.0109981	−	0.0410455i	−0.971207	+	0.238238i	$0.923430\pi$
$858$		0			0
$859$	−26.9630	+	35.1388i	−0.919964	+	1.19892i	0.0596877	+	0.998217i	$0.480990\pi$
$859$	−26.9630	+	35.1388i	−0.919964	+	1.19892i	−0.979652	+	0.200704i	$0.935677\pi$
$860$		0			0
$861$	3.57551	−	2.54989i	0.121853	−	0.0869000i
$862$		0			0
$863$	−3.72247	−	6.44751i	−0.126714	−	0.219476i	0.795687	−	0.605707i	$-0.207110\pi$
$863$	−3.72247	−	6.44751i	−0.126714	−	0.219476i	−0.922402	+	0.386232i	$0.873776\pi$
$864$		0			0
$865$	−11.7964	+	20.4319i	−0.401089	+	0.694707i
$866$		0			0
$867$	1.88171	+	0.779431i	0.0639063	+	0.0264709i
$868$		0			0
$869$	5.04115	+	12.1704i	0.171009	+	0.412853i
$870$		0			0
$871$	−12.6294	−	47.1334i	−0.427930	−	1.59706i
$872$		0			0
$873$	−10.4326	+	38.9351i	−0.353091	+	1.31775i
$874$		0			0
$875$	29.7022	−	11.1021i	1.00412	−	0.375319i
$876$		0			0
$877$	−11.9811	+	1.57734i	−0.404573	+	0.0532630i	−0.330067	−	0.943958i	$-0.607071\pi$
$877$	−11.9811	+	1.57734i	−0.404573	+	0.0532630i	−0.0745058	+	0.997221i	$0.523738\pi$
$878$		0			0
$879$	3.20718	+	1.85167i	0.108176	+	0.0624552i
$880$		0			0
$881$		−	13.4643i		−	0.453624i	−0.973939	−	0.226812i	$-0.927170\pi$
$881$		−	13.4643i		−	0.453624i	0.973939	−	0.226812i	$-0.0728303\pi$
$882$		0			0
$883$	−11.4908	+	27.7413i	−0.386697	+	0.933569i	0.603938	+	0.797031i	$0.293598\pi$
$883$	−11.4908	+	27.7413i	−0.386697	+	0.933569i	−0.990635	+	0.136538i	$0.956402\pi$
$884$		0			0
$885$	0.197235	−	1.49815i	0.00662998	−	0.0503597i
$886$		0			0
$887$	0.00559196	−	0.0208695i	0.000187760	−	0.000700728i	−0.965832	−	0.259169i	$-0.916551\pi$
$887$	0.00559196	−	0.0208695i	0.000187760	−	0.000700728i	0.966020	+	0.258469i	$0.0832179\pi$
$888$		0			0
$889$	17.1827	−	16.0201i	0.576288	−	0.537298i
$890$		0			0
$891$	30.3402	−	39.5401i	1.01643	−	1.32464i
$892$		0			0
$893$	50.7994	−	38.9797i	1.69994	−	1.30441i
$894$		0			0
$895$	−31.0002			−1.03622
$896$		0			0
$897$	−0.683993			−0.0228379
$898$		0			0
$899$	9.58237	−	7.35281i	0.319590	−	0.245230i
$900$		0			0
$901$	−6.56539	+	8.55619i	−0.218725	+	0.285048i
$902$		0			0
$903$	0.334894	+	1.45119i	0.0111446	+	0.0482927i
$904$		0			0
$905$	−4.69524	+	17.5229i	−0.156075	+	0.582480i
$906$		0			0
$907$	−5.23336	+	39.7513i	−0.173771	+	1.31992i	0.652989	+	0.757367i	$0.273515\pi$
$907$	−5.23336	+	39.7513i	−0.173771	+	1.31992i	−0.826760	+	0.562554i	$0.809819\pi$
$908$		0			0
$909$	−1.31042	+	3.16363i	−0.0434638	+	0.104931i
$910$		0			0
$911$			54.0446i			1.79058i	0.445486	+	0.895289i	$0.353031\pi$
$911$			54.0446i			1.79058i	−0.445486	+	0.895289i	$0.646969\pi$
$912$		0			0
$913$	−72.3274	−	41.7583i	−2.39369	−	1.38200i
$914$		0			0
$915$	−0.497492	+	0.0654960i	−0.0164466	+	0.00216523i
$916$		0			0
$917$	6.46928	+	5.33386i	0.213634	+	0.176140i
$918$		0			0
$919$	−8.62664	+	32.1950i	−0.284566	+	1.06202i	0.664589	+	0.747209i	$0.268607\pi$
$919$	−8.62664	+	32.1950i	−0.284566	+	1.06202i	−0.949156	+	0.314807i	$0.898060\pi$
$920$		0			0
$921$	0.201078	+	0.750432i	0.00662574	+	0.0247276i
$922$		0			0
$923$	−9.51233	−	22.9648i	−0.313102	−	0.755896i
$924$		0			0
$925$	2.75483	+	1.14109i	0.0905781	+	0.0375187i
$926$		0			0
$927$	17.8164	−	30.8589i	0.585168	−	1.01354i
$928$		0			0
$929$	−24.1646	−	41.8543i	−0.792815	−	1.37320i	−0.924218	−	0.381866i	$-0.875281\pi$
$929$	−24.1646	−	41.8543i	−0.792815	−	1.37320i	0.131403	−	0.991329i	$-0.458052\pi$
$930$		0			0
$931$	−2.25662	−	37.0070i	−0.0739578	−	1.21285i
$932$		0			0
$933$	1.07538	−	1.40146i	0.0352063	−	0.0458817i
$934$		0			0
$935$	4.79020	+	17.8773i	0.156656	+	0.584649i
$936$		0			0
$937$	−32.3158	−	32.3158i	−1.05571	−	1.05571i	−0.998354	−	0.0573576i	$-0.981732\pi$
$937$	−32.3158	−	32.3158i	−1.05571	−	1.05571i	−0.0573576	−	0.998354i	$-0.518268\pi$
$938$		0			0
$939$	−3.74300	+	1.55040i	−0.122148	+	0.0505954i
$940$		0			0
$941$	36.6613	+	47.7780i	1.19513	+	1.55752i	0.749036	+	0.662530i	$0.230517\pi$
$941$	36.6613	+	47.7780i	1.19513	+	1.55752i	0.446090	+	0.894988i	$0.352816\pi$
$942$		0			0
$943$	−11.1029	+	6.41023i	−0.361559	+	0.208746i
$944$		0			0
$945$	−3.98342	+	2.11755i	−0.129581	+	0.0688840i
$946$		0			0
$947$	−15.7284	+	2.07069i	−0.511106	+	0.0672884i	−0.381669	−	0.924299i	$-0.624650\pi$
$947$	−15.7284	+	2.07069i	−0.511106	+	0.0672884i	−0.129437	+	0.991588i	$0.541317\pi$
$948$		0			0
$949$	−5.01509	+	38.0934i	−0.162797	+	1.23656i
$950$		0			0
$951$	−0.164990	−	0.164990i	−0.00535017	−	0.00535017i
$952$		0			0
$953$	−9.83973	+	9.83973i	−0.318740	+	0.318740i	−0.848283	−	0.529543i	$-0.822363\pi$
$953$	−9.83973	+	9.83973i	−0.318740	+	0.318740i	0.529543	+	0.848283i	$0.322363\pi$
$954$		0			0
$955$	−9.97524	−	1.31327i	−0.322791	−	0.0424963i
$956$		0			0
$957$	−0.547536	−	4.15895i	−0.0176993	−	0.134440i
$958$		0			0
$959$	−12.8271	+	20.5234i	−0.414208	+	0.662736i
$960$		0			0
$961$	12.8285	+	22.2197i	0.413824	+	0.716763i
$962$		0			0
$963$	−6.39852	+	4.90976i	−0.206189	+	0.158215i
$964$		0			0
$965$	2.63418	+	6.35946i	0.0847971	+	0.204718i
$966$		0			0
$967$	−19.8740	+	19.8740i	−0.639105	+	0.639105i	−0.950335	−	0.311230i	$-0.899259\pi$
$967$	−19.8740	+	19.8740i	−0.639105	+	0.639105i	0.311230	+	0.950335i	$0.399259\pi$
$968$		0			0
$969$	−1.18561	+	0.317684i	−0.0380874	+	0.0102055i
$970$		0			0
$971$	17.1782	+	13.1813i	0.551276	+	0.423009i	0.846476	−	0.532427i	$-0.178720\pi$
$971$	17.1782	+	13.1813i	0.551276	+	0.423009i	−0.295201	+	0.955435i	$0.595386\pi$
$972$		0			0
$973$	4.68335	−	10.2742i	0.150141	−	0.329375i
$974$		0			0
$975$	0.523978	−	0.302519i	0.0167807	−	0.00968836i
$976$		0			0
$977$	13.0679	+	7.54477i	0.418080	+	0.241379i	0.694256	−	0.719729i	$-0.255734\pi$
$977$	13.0679	+	7.54477i	0.418080	+	0.241379i	−0.276175	+	0.961107i	$0.589067\pi$
$978$		0			0
$979$	−0.853615	+	2.06081i	−0.0272817	+	0.0658637i
$980$		0			0
$981$	47.7392	−	19.7742i	1.52420	−	0.631342i
$982$		0			0
$983$	37.6933	−	10.0999i	1.20223	−	0.322136i	0.398521	−	0.917159i	$-0.369524\pi$
$983$	37.6933	−	10.0999i	1.20223	−	0.322136i	0.803709	+	0.595023i	$0.202857\pi$
$984$		0			0
$985$	−1.40803	−	0.377279i	−0.0448634	−	0.0120211i
$986$		0			0
$987$	1.59076	+	4.25588i	0.0506345	+	0.135466i
$988$		0			0
$989$	−0.567506	−	4.31063i	−0.0180456	−	0.137070i
$990$		0			0
$991$	7.09323	−	12.2858i	0.225324	−	0.390272i	−0.731093	−	0.682278i	$-0.760989\pi$
$991$	7.09323	−	12.2858i	0.225324	−	0.390272i	0.956417	+	0.292006i	$0.0943227\pi$
$992$		0			0
$993$	1.37758			0.0437161
$994$		0			0
$995$	0.134583	+	0.0557462i	0.00426658	+	0.00176727i
$996$		0			0
$997$	28.1786	+	3.70979i	0.892426	+	0.117490i	0.562773	−	0.826612i	$-0.309735\pi$
$997$	28.1786	+	3.70979i	0.892426	+	0.117490i	0.329654	+	0.944102i	$0.393068\pi$
$998$		0			0
$999$	−2.52087	−	0.675465i	−0.0797567	−	0.0213708i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	896.2.bh.a.81.15		240
4.3	odd	2		224.2.bd.a.221.29	yes	240
7.2	even	3	inner	896.2.bh.a.849.15		240
28.23	odd	6		224.2.bd.a.93.8	yes	240
32.11	odd	8		224.2.bd.a.53.8	✓	240
32.21	even	8	inner	896.2.bh.a.305.15		240
224.107	odd	24		224.2.bd.a.149.29	yes	240
224.149	even	24	inner	896.2.bh.a.177.15		240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
224.2.bd.a.53.8	✓	240	32.11	odd	8
224.2.bd.a.93.8	yes	240	28.23	odd	6
224.2.bd.a.149.29	yes	240	224.107	odd	24
224.2.bd.a.221.29	yes	240	4.3	odd	2
896.2.bh.a.81.15		240	1.1	even	1	trivial
896.2.bh.a.177.15		240	224.149	even	24	inner
896.2.bh.a.305.15		240	32.21	even	8	inner
896.2.bh.a.849.15		240	7.2	even	3	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 896 = 2^{7} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	896.bh (of order \(24\), degree \(8\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.112695 + 0.0864738i) q^{3} +(1.22200 - 1.59255i) q^{5} +(1.93515 - 1.80422i) q^{7} +(-0.771235 + 2.87829i) q^{9} +O(q^{10})\)	\(q+(-0.112695 + 0.0864738i) q^{3} +(1.22200 - 1.59255i) q^{5} +(1.93515 - 1.80422i) q^{7} +(-0.771235 + 2.87829i) q^{9} +(-0.737665 + 5.60312i) q^{11} +(-1.67953 + 4.05474i) q^{13} +0.285143i q^{15} +(1.41287 + 0.815720i) q^{17} +(5.25122 - 0.691336i) q^{19} +(-0.0620631 + 0.370666i) q^{21} +(0.283964 - 1.05977i) q^{23} +(0.251185 + 0.937436i) q^{25} +(-0.325061 - 0.784767i) q^{27} +(4.82760 + 1.99966i) q^{29} +(1.15574 - 2.00180i) q^{31} +(-0.401392 - 0.695231i) q^{33} +(-0.508549 - 5.28657i) q^{35} +(1.87037 - 2.43752i) q^{37} +(-0.161354 - 0.602183i) q^{39} +(-8.26270 - 8.26270i) q^{41} +(3.66118 - 1.51651i) q^{43} +(3.64135 + 4.74550i) q^{45} +(10.4696 - 6.04464i) q^{47} +(0.489578 - 6.98286i) q^{49} +(-0.229761 + 0.0302486i) q^{51} +(-0.862860 + 6.55407i) q^{53} +(8.02180 + 8.02180i) q^{55} +(-0.532003 + 0.532003i) q^{57} +(-5.25402 - 0.691705i) q^{59} +(0.229695 + 1.74471i) q^{61} +(3.70061 + 6.96138i) q^{63} +(4.40497 + 7.62963i) q^{65} +(-8.82073 + 6.76838i) q^{67} +(0.0596408 + 0.143986i) q^{69} +(-4.00484 + 4.00484i) q^{71} +(8.45624 - 2.26584i) q^{73} +(-0.109371 - 0.0839233i) q^{75} +(8.68177 + 12.1738i) q^{77} +(2.01864 - 1.16546i) q^{79} +(-7.63731 - 4.40940i) q^{81} +(-5.65524 + 13.6529i) q^{83} +(3.02560 - 1.25324i) q^{85} +(-0.716964 + 0.192110i) q^{87} +(0.381246 + 0.102154i) q^{89} +(4.06551 + 10.8767i) q^{91} +(0.0428573 + 0.325534i) q^{93} +(5.31602 - 9.20762i) q^{95} +13.5272 q^{97} +(-15.5585 - 6.44453i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q + 4 q^{3} - 4 q^{5} + 8 q^{7} - 4 q^{9}+O(q^{10}) \) 240 * q + 4 * q^3 - 4 * q^5 + 8 * q^7 - 4 * q^9	\( 240 q + 4 q^{3} - 4 q^{5} + 8 q^{7} - 4 q^{9} + 4 q^{11} - 16 q^{13} + 4 q^{19} - 8 q^{21} + 12 q^{23} - 4 q^{25} + 16 q^{27} - 16 q^{29} + 56 q^{31} - 8 q^{33} + 32 q^{35} - 4 q^{37} + 4 q^{39} - 16 q^{41} + 8 q^{45} + 28 q^{51} - 20 q^{53} + 16 q^{55} - 16 q^{57} + 36 q^{59} - 4 q^{61} + 16 q^{63} - 8 q^{65} - 36 q^{67} - 16 q^{69} - 48 q^{71} - 4 q^{73} - 16 q^{75} - 8 q^{77} + 96 q^{83} - 56 q^{85} + 4 q^{87} - 4 q^{89} + 56 q^{91} + 20 q^{93} + 8 q^{95} - 32 q^{97} - 8 q^{99}+O(q^{100}) \) 240 * q + 4 * q^3 - 4 * q^5 + 8 * q^7 - 4 * q^9 + 4 * q^11 - 16 * q^13 + 4 * q^19 - 8 * q^21 + 12 * q^23 - 4 * q^25 + 16 * q^27 - 16 * q^29 + 56 * q^31 - 8 * q^33 + 32 * q^35 - 4 * q^37 + 4 * q^39 - 16 * q^41 + 8 * q^45 + 28 * q^51 - 20 * q^53 + 16 * q^55 - 16 * q^57 + 36 * q^59 - 4 * q^61 + 16 * q^63 - 8 * q^65 - 36 * q^67 - 16 * q^69 - 48 * q^71 - 4 * q^73 - 16 * q^75 - 8 * q^77 + 96 * q^83 - 56 * q^85 + 4 * q^87 - 4 * q^89 + 56 * q^91 + 20 * q^93 + 8 * q^95 - 32 * q^97 - 8 * q^99

Introduction

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